Violation of a causal inequality in a spacetime with definite causal order

TL;DR

This paper demonstrates that within Minkowski spacetime, the causal indeterminacy of quantum fields can lead to violations of causal inequalities, challenging classical notions of fixed causal order.

Contribution

It introduces a Gaussian-localised field theoretic framework to show causal inequality violations in Minkowski spacetime, highlighting the role of quantum field indeterminacy.

Findings

Causal inequalities can be violated in Minkowski spacetime using quantum fields.

The causal indeterminacy of fields enables violations without indefinite causal structure.

Optimal observer arrangements for maximal violation are identified.

Abstract

Processes with an indefinite causal structure may violate a causal inequality, which quantifies quantum correlations that arise from a lack of causal order. In this paper, we show that when the inequalities are analysed with a Gaussian-localised field theoretic definition of particles and labs, the causal indeterminacy of the fields themselves allows a causal inequality to be violated within the causal structure of Minkowski spacetime. We quantify the violation of the inequality and determine the optimal ordering of observers.